Monday March 22, 2010
This problem provides some insight into the world of pharmaceuticals.

A typical pharmaceutical problem is to determine the minimum effective concentration (MEC) and the maximum therapeutic concentration (MTC) for a given drug. Typically, these values are relative to the percent of the drug being carried in the blood stream, the blood serum level. A value below the MEC means that the drug is not producing the desired effect. A value above the MTC means that you start moving towards very bad things that might happen, such as permanent tissue/organ damage or death.

A two-compartment mathematical model is typically used with a drug taken orally, where the first compartment represents the stomach where the drug dissolves, transitioning to the second compartment, which represents the blood volume of the person.

The pharmaceutical companies will typically give you the half-life for the drug. This is the time it takes for half of the drug to be eliminated from the body. The computational scientist uses this value, along with the formula for exponential decay, to determine the drug elimination constant (or elimination rate constant), which in turn helps define a drug's dosing level, producing blood serum concentrations that quickly rise above the MEC and always stay below the MTC. In fact, the computational scientist will notice that there is a geometric sequence that the blood serum level will approach, but never surpass.

An additional factor to take into consideration is that different sized people have different volumes of blood in their systems and hence different blood serum levels. These ranges are taken into account when a general dosing pattern is stated for a particular drug.


You are to propose and justify a dosing pattern for the medical situation defined below.

Even the experts do not agree on the correct answer to the open-ended problem that follows, but that will not stop us from assigning you the very same problem. Your analysis method and the justification for that method are critical to your solution of this problem.

A mother discovers she is pregnant. She requires the selective serotonin reuptake inhibitor (SSRI), Celexa (Citalopram Hydrobromide), for her emotional well being. She is justifiably concerned the drug will pass through the placenta to her fetus and potentially cause harm. She has heard rumors that Celexa can affect the stillborn rate and appearance of birth defects in her child.

Using the computational tools, libraries, languages, and computing resources at your disposal, determine if there is a possible dosing pattern allowing this young mother-to-be to continue with Celexa while she is pregnant and without harming her soon-to-be child.

Specifically, you want to achieve a dosing pattern where Celexa reaches the MEC for the mother and stays between there and the MTC. The fetus can never have a level of the drug reaching MEC, which can affect the stillborn rate and appearance of birth defects.

You can obtain some relevant information about Celexa here and here.

You will need to research Celexa via the web to determine its pharmaceutical properties. You will need to consider the number of compartments desired for the model and the drug flow rates between compartments. Possible factors affecting these choices are:

* Stomach to blood transition
* Blood to brain transition
* Placental transition

You will also need to consider the affect of body sizes and types:

* Ranges of blood serum volumes of different sized women
* Ranges of blood serum volumes of different sized fetuses
* Ranges of blood serum volumes during fetal development
* Effect of a multiple fetus pregnancy

You will also need to determine the drug elimination constant.

You will have to consider whether you choose some pre-existing application, or code your own solver.

-Additional resources which may prove helpful are as follows:

General Pharmacological Facts
General Overview of Fetal Growth
More Information on Fetal Growth
Chemical studies with a similar compound
Celexa Product Information


When you have run your data sets through your model, please analyze your results to determine the dosing pattern(s) that work, as well as the characteristics of the mothers and fetuses for which it works.

You should include the rationale for the model, the results obtained from running the model, and a description of the steps taken in working to gather results. State the problems encountered, the possible solutions considered and tried, and the solution that was used. Your report should also include observations on additional steps that might be taken to improve the speed of the execution of your code.
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